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Irreducible
character restrictions to maximal subgroups of low-rank
classical groups of types $B$ and $C$
Kempton Albee, Mike Barnes, Aaron Parker, Eric Roon and A. A. Schaeffer Fry
Vol. 12 (2019), No. 4, 607–631
DOI: 10.2140/involve.2019.12.607
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Abstract |
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Representations are special functions on groups that give us a way to study abstract groups using matrices, which are often easier to understand. In particular, we are often interested in irreducible representations, which can be thought of as the building blocks of all representations. Much of the information about these representations can then be understood by instead looking at the trace of the matrices, which we call the character of the representation. This paper will address restricting characters to subgroups by shrinking the domain of the original representation to just the subgroup. In particular, we will discuss the problem of determining when such restricted characters remain irreducible for certain low-rank classical groups. |
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Keywords
irreducible characters, classical groups
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Mathematical Subject Classification 2010
Primary: 20C15, 20C33
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Milestones
Received: 12 February 2018
Revised: 11 October 2018
Accepted: 12 October 2018
Published: 16 April 2019
Communicated by Scott T. Chapman
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Authors |
| Kempton Albee | |
| Metropolitan State University of
Denver Denver, CO United States |
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| Mike Barnes | |
| Metropolitan State University of
Denver Denver, CO United States |
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| Aaron Parker | |
| Metropolitan State University of
Denver Denver, CO United States |
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| Eric Roon | |
| University of Arizona Tucson, AZ United States |
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| A. A. Schaeffer Fry | |
| Department of Mathematical and
Computer Sciences Metropolitan State University of Denver Denver, CO United States |
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